The general objective is to study several empirical and theoretical facets of stimulus-class formation. Matching to sample provides the specific context within which the development of stimulus classes is to be studied and features of the matching paradigm itself will also come under scrutiny both with children and with nonhuman species as subjects. Our analysis of stimulus classes specifies three kinds of relations that must exist among equivalent elements of any class: Reflexivity, Symmetry, and Transitivity. It is proposed that when an arbitrary matching-to-sample procedure generates these relations among the sample and comparison stimuli, the subject's performance can be considered true matching, and can be used as a model for studying the development of simple language skills; when these relations are not generated, the subject's performance must be considered to be nonlinguistic. Independent experimental tests of each aspect of stimulus equivalence are to be carried out in order to determine the adequacy of the logical analysis.